Large-scale Instances Research Articles

Outpatient scheduling problem in smart hospital with two-agent deep reinforcement learning algorithm

As the internet and digital technologies revolutionize the healthcare sector, the development of smart hospitals is pivotal for improving medical service efficiency. This research presents a mathematical model for the outpatient scheduling problem and introduces the Graph-based Two-Agent Deep Reinforcement Learning algorithm (GTARS-DRL) to address the escalating demand for medical services and the scarcity of resources. The GTARS-DRL leverages graph neural networks for feature extraction of patient medical activities and applies the PDQPN algorithm to train agents for optimizing patient sequencing and service desk allocation, effectively minimizing wait times. Our experiments indicate that GTARS-DRL outperforms traditional scheduling rules in solution quality and matches the performance of Genetic Algorithms (GA), with a notable advantage in computational efficiency, boasting an ACPU of 0.762 s and an ARPT of 0.327 s. The algorithm’s efficacy is further supported by its successful application to larger-scale instances, showcasing its potential for real-world use. This study contributes a novel approach to outpatient scheduling in smart hospitals, providing theoretical backing and practical direction for the optimization of medical resource allocation, and is poised to significantly enhance service efficiency and patient satisfaction.

A two-echelon multi-trip vehicle routing problem with synchronization for an integrated water- and land-based transportation system

This study focuses on two-echelon synchronized logistics problems in the context of integrated water- and land-based transportation (IWLT) systems. The aim is to meet the increasing demand in city logistics as a result of the growth in transport activities, including parcel delivery, food delivery, and waste collection. We propose two models, a novel mixed integer linear joint model, and a logic-based Benders’ decomposition (LBBD) model, for a two-echelon problem under realistic settings such as multi-trips, time windows, and synchronization at the satellites with no storage and limited resource capacities. The objective is to optimize transfers and satellite assignments, thereby reducing overall logistics costs for street vehicles and vessels. Computational experiments demonstrate that the LBBD model is more robust in terms of solution quality and solution time on average while the added value of the LBBD is more evident when solving large-scale instances with 100 customers, reducing the overall costs by 10.6% on average and significantly reducing the fleet costs on both networks. Furthermore, we assess the effect of changing cost parameters and satellite locations in the proposed IWLT system–analyzing system behavior and suggesting potential improvements–and evaluate several system alternatives in city logistics–consisting of different transportation network designs (single- and two-echelon), vehicle types, and operational constraints. On average, the proposed two-echelon IWLT system reduces the number of kilometers traveled by vehicles at street level by ranging from 20% to 30% compared to a typical single-echelon service design that relies solely on trucks.

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Single machine scheduling aims at determining the job sequence with the best desired performance, and provides the basic building block for more advanced scheduling problems. In the present study, a single machine scheduling model with uncertain processing time is considered by incorporating the job release time and due date. The job processing time follows unknown probability distribution, and can be estimated via the historical data. To model the uncertainty, the processing time distribution is defined over a Wasserstein ball ambiguity set, which covers all feasible probability distributions within the confidence radius of the empirical distribution, known as the center of the ball. Then a data-driven distributionally robust scheduling model is constructed with individual chance constraints. In particular, two equivalent reformulations are derived with respect to the ℓ1-norm and ℓ2-norm metrics of the Wasserstein ball, namely, a mixed-integer linear programming and a mixed-integer second order cone programming model, respectively. To accelerate the solving of large-scale instances, a tailored constraint generation algorithm is introduced. In the numerical analysis, the proposed distributionally robust scheduling approach is compared with the state-of-the-art methods in terms of out-of-sample performance.

Re-Supplying Autonomous Mobile Parcel Lockers in Last-Mile Distribution

This paper investigates a practical last-mile delivery scenario where a fleet of trucks replenishes autonomous mobile parcel lockers (AMPLs) in an urban setting. The lockers move along specified paths within restricted zones to reach customers’ locations. Ensuring seamless coordination between trucks and AMPLs requires the identification of suitable locations to exchange empty or loaded modular lockers. We first introduce a mixed-integer linear programming (MILP) formulation for the investigated problem. The proposed formulation establishes the basis for optimizing meeting point selection and routing decisions. Additionally, the study introduces a cluster-based simulated annealing (CSA) algorithm tailored for addressing larger-scale instances of the studied problem. The CSA algorithm incorporates the K-means clustering method with specialized operators rooted in an extensive neighborhood search, aiming to improve the effectiveness of solution discovery. We generated a new set of benchmark instances to assess the MILP formulation’s efficiency and the proposed metaheuristic algorithm and conducted comprehensive numerical experiments.

List-Based Threshold Accepting Algorithm with Improved Neighbor Operator for 0–1 Knapsack Problem

The list-based threshold accepting (LBTA) algorithm is a sophisticated local search method that utilizes a threshold list to streamline the parameter tuning process in the traditional threshold accepting (TA) algorithm. This paper proposes an enhanced local search version of the LBTA algorithm specifically tailored for solving the 0–1 knapsack problem (0–1 KP). To maintain a dynamic threshold list, a feasible threshold updating strategy is designed to accept adaptive modifications during the search process. In addition, the algorithm incorporates an improved bit-flip operator designed to generate a neighboring solution with a controlled level of disturbance, thereby fostering exploration within the solution space. Each trial solution produced by this operator undergoes a repair phase using a hybrid greedy repair operator that incorporates both density-based and value-based add operator to facilitate optimization. The LBTA algorithm’s performance was evaluated against several state-of-the-art metaheuristic approaches on a series of large-scale instances. The simulation results demonstrate that the LBTA algorithm outperforms or is competitive with other leading metaheuristics in the field.

A Novel Approach for Solving the N-Queen Problem Using a Non-Sequential Conflict Resolution Algorithm

The N-Queens problem is a fundamental challenge in combinatorial optimization, commonly used as a benchmark for assessing the efficiency of algorithms. Traditional algorithms, such as Backtracking with Forward Checking (BFC), constraint satisfaction problem (CSP) techniques, Lookahead algorithms, and heuristic-based methods, often face challenges with exponential time complexity, making them less practical for large-scale instances. This paper introduces a novel algorithm, non-sequential conflict resolution (NSCR), which improves performance over traditional algorithms through dynamic conflict resolution. The NSCR algorithm iteratively resolves conflicts among queens by adjusting their positions, aiming to optimize both time complexity and memory usage. While NSCR also operates within exponential time bounds, it demonstrates improved scalability and efficiency compared to traditional methods. A significant strength of the NSCR algorithm lies in its space complexity, which is O(n), and a time complexity that, while typically lower than traditional methods, can reach O(n3) in the worst-case scenario. This linear space complexity is highly advantageous, particularly when dealing with large problem sizes, as it ensures efficient use of memory resources. Comparative analysis with the aforementioned algorithms shows that NSCR offers superior resource management, using up to 60% less memory and reducing runtime by approximately 50%, making it an efficient option for large-scale instances of the N-Queens problem. The algorithm’s performance, evaluated on problem sizes ranging from 8 to 1000 queens, highlights its ability to manage computational resources effectively, despite the inherent challenges of exponential time complexity.

Solving large-scale instances of the urban transit routing problem with a parallel artificial bee colony-hill climbing optimization algorithm

Swarm Intelligence simulates the collective behavior of decentralized and self-organized swarms. One of the main relevant methods is the Artificial Bee Colony (ABC) algorithm which simulates the foraging behavior of bee swarms in a colony to produce efficient solutions to various problems. The Urban Transit Routing Problem (UTRP) involves finding an efficient set of routes in a transit network to satisfy travel demand subject to operational and budget constraints. It is a complex, NP-Hard problem, in which otherwise correct solutions can be rejected because of impracticability. In this study, a hybrid algorithm consisting of a parallel ABC and Hill Climbing was used to find quality solutions to the UTRP. Thorough comparative results on Mandl’s well-known instance and Mumford’s large-scale instances demonstrate that the proposed algorithm outperforms existing techniques, achieving high levels of direct trip coverage in small computational times. Remarkably, when applied to the most extensive benchmark comprising over 6 million trips and 60 bus routes, the proposed algorithm demonstrates an impressive 11 % enhancement in direct coverage over the previously best-reported results, allowing the design of real-world bus networks in under 3 hours.

An Algorithm for Clustering with Confidence-Based Must-Link and Cannot-Link Constraints

We study here the semisupervised k-clustering problem where information is available on whether pairs of objects are in the same or different clusters. This information is available either with certainty or with a limited level of confidence. We introduce the pair-wise confidence constraints clustering (PCCC) algorithm, which iteratively assigns objects to clusters while accounting for the information provided on the pairs of objects. Our algorithm uses integer programming for the assignment of objects, which allows us to include relationships as hard constraints that are guaranteed to be satisfied or as soft constraints that can be violated subject to a penalty. This flexibility distinguishes our algorithm from the state of the art, in which all pair-wise constraints are considered hard or all are considered soft. We developed an enhanced multistart approach and a model-size reduction technique for the integer program that contribute to the effectiveness and efficiency of the algorithm. Unlike existing algorithms, our algorithm scales to large-scale instances with up to 60,000 objects, 100 clusters, and millions of cannot-link constraints (which are the most challenging constraints to incorporate). We compare the PCCC algorithm with state-of-the-art approaches in an extensive computational study. Even though the PCCC algorithm is more general than the state-of-the-art approaches in its applicability, it outperforms the state-of-the-art approaches on instances with all hard or all soft constraints in terms of both run time and various metrics of solution quality. The code of the PCCC algorithm is publicly available on GitHub. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: The research of D. S. Hochbaum was supported by the AI Institute NSF Award [Grant 2112533]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0419 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0419 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Green logistics optimization for coal supply in a power plant connecting maritime port

This study addresses the coal transportation and flow distribution challenges within a “port-before-plant” type thermal power plant, with a strong emphasis on green logistics principles. Despite significant advancements in clean energy, coal remains a dominant energy source in China, necessitating optimization in its usage and management to mitigate environmental impacts. This paper introduces an integrated optimization model grounded in green logistics and employs an Improved Particle Swarm Optimization (IPSO) algorithm to efficiently manage the coal supply chain from unloading at ports to loading into generators. The model incorporates new parameters and constraints that not only reflect the operational realities of coal logistics but also emphasize minimizing carbon emissions and energy consumption. Numerical experiments demonstrate the algorithm’s superior performance compared to traditional solvers like Gurobi, particularly in handling large-scale instances. Sensitivity analysis reveals the importance of prioritizing efficient and environmentally sustainable unloading and loading equipment, suggesting strategies for optimizing green coal transportation routes. Overall, this research provides valuable insights for policymakers and industry operators to enhance operational efficiency while ensuring environmental sustainability through the implementation of green logistics

Divide-and-conquer initialization and mutation operators for the large-scale mixed Capacitated Arc Routing Problem

As cities continue to grow, thus will the size of the routing problems necessary to the functioning of all cities. Applications such as waste collection, road maintenance, or winter gritting span over an entire city, therefore algorithms must be designed to solve large-scale problems. The Capacitated Arc Routing Problem (CARP) is an important combinatorial optimization problem that is typically used to model these applications. Classical algorithms for CARP struggle to find quality solutions for large-scale instances with thousands of services within a reasonable computational budget. To address the issue of scalability, several divide-and-conquer heuristics have recently been proposed. In this paper, we propose to integrate divide-and-conquer heuristics into a memetic algorithm by adapting these as an initialization method and as a mutation operator. The resulting algorithm, which we call Memetic Algorithm with Divide-and-Conquer Mutation (MADCoM), outperforms state-of-the-art algorithms on large-scale instances and new best solutions are found for 17 instances of MCARP, 2 of which are optimal solutions, and for 23 large-scale CARP instances. These results demonstrate the potential of the integration of divide-and-conquer heuristics into metaheuristics as a strategy to efficiently solve large-scale problems.

An Improved Driving Training-Based Optimization Algorithm for the Minimum Gap Graph Connected Partition Problem

In this paper, we consider the minimum gap partition problem in an undirected connected graph with nonnegative vertex weights. This problem involves in dividing the given graph into a specified number of connected subgraphs such that the total difference between the largest and the smallest vertex weights in each subgraph is minimized. Namely, let G = (V, E, W) be a given undirected connected graph with vertex set V , edge set E, and nonnegative vertex weight function W : V → R+, and let k ≥ 2 be a given positive integer. The minimum gap partition problem consists of constructing a partition P = {V1, V2, . . . , Vk} of non-empty and pairwise disjoint subsets of V such that each vertex set Vi, i = 1, 2, . . . , k, induces a connected subgraph G[Vi] of G. The objective of the problem is to find such a partition of V that minimizes the total difference 1≤i≤k maxv∈Viw(v) − minv∈Viw(v). This problem, as many other variants of graph partition problems, is known to be NP-hard problem. We designed an efficient metaheuristic algorithm for finding approximate solution of large-scale instances of this problem. The quality of the proposed algorithm is assessed comparing with the previous algorithms proposed for the problem.

Scheduling of memory chips for final testing on parallel machines considering power constraints and deteriorating effects

This paper delves into the intricate scheduling strategies crucial for the final testing phase of memory chip manufacturing within the semiconductor industry and other related sectors. It specifically addresses the complex serial-batching scheduling problem, where memory chips are tested on parallel machines under power constraints and chip deterioration effects. The processing time for each chip is significantly influenced by both the cumulative processing time of preceding chips and the power requirements for testing. We formulate this real-world optimization problem using a mixed integer nonlinear programming model. Exact solutions for small instances are obtained using a commercial solver. However, due to the model's complexity, we also develop heuristic solutions to efficiently handle larger instances. Based on the derivation of structural properties, we develop two tailored heuristic algorithms to determine the schedule for the final testing of memory chips. Additionally, we propose a refined Variable Neighborhood Search algorithm (VNS-H) that seamlessly integrates five local search strategies with two supplementary heuristic algorithms, dynamically alternating between them to ensure a balance between computational efficiency and the quality of the solutions obtained. Additionally, we establish a lower bound to validate the effectiveness of these solutions, particularly for large-scale instances. To validate the efficacy and robustness of our proposed metaheuristic algorithm, we conduct a rigorous comparison of the VNS-H algorithm with five other metaheuristic algorithms that have promising performance in various optimization problems. The results highlight the superior performance of the VNS-H algorithm. In small-scale instances, our VNS-H algorithm achieves an average makespan that is 5.52% lower compared to the original VNS. For large-scale instances, the VNS-H algorithm reduces the average makespan by 13.46% compared to VNS. Finally, we discuss the managerial implications of our findings, providing insights specifically tailored to semiconductor manufacturing enterprises based on the outcomes of this study.

A Deep Reinforcement Learning Method Based on a Transformer Model for the Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem (FJSSP), which can significantly enhance production efficiency, is a mathematical optimization problem widely applied in modern manufacturing industries. However, due to its NP-hard nature, finding an optimal solution for all scenarios within a reasonable time frame faces serious challenges. This paper proposes a solution that transforms the FJSSP into a Markov Decision Process (MDP) and employs deep reinforcement learning (DRL) techniques for resolution. First, we represent the state features of the scheduling environment using seven feature vectors and utilize a transformer encoder as a feature extraction module to effectively capture the relationships between state features and enhance representation capability. Second, based on the features of the jobs and machines, we design 16 composite dispatching rules from multiple dimensions, including the job completion rate, processing time, waiting time, and manufacturing resource utilization, to achieve flexible and efficient scheduling decisions. Furthermore, we project an intuitive and dense reward function with the objective of minimizing the total idle time of machines. Finally, to verify the performance and feasibility of the algorithm, we evaluate the proposed policy model on the Brandimarte, Hurink, and Dauzere datasets. Our experimental results demonstrate that the proposed framework consistently outperforms traditional dispatching rules, surpasses metaheuristic methods on larger-scale instances, and exceeds the performance of existing DRL-based scheduling methods across most datasets.

On convergence of a q-random coordinate constrained algorithm for non-convex problems

We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates simultaneously in each iteration of a coordinate descent algorithm, our algorithm allows updating arbitrary number of coordinates. We provide a proof of convergence of the algorithm. The convergence rate of the algorithm improves when we update more coordinates per iteration. Numerical experiments on large scale instances of different optimization problems show the benefit of updating many coordinates simultaneously.

Two stage Ordered Escape Routing combined with LP and heuristic algorithm for large scaled PCB

The Ordered Escape Routing (OER) problem, which is an NP-hard problem, is critical to PCB design. Primary methods based on integer linear programming (ILP) work well on small-scale PCBs with fewer pins. However, when dealing with large-scale instances, traditional ILP strategies frequently cause time violations as the number of variables increases due to time-consuming preprocessing. In addition, heuristic algorithms have a time advantage when dealing with specific problems. In this paper, We propose an efficient two-stage escape routing method that employs LP for global routing and uses a heuristic algorithm to deal with the path intersection problem to minimize wiring length and runtime for large-scale PCBs. We first model the OER problem as a min-cost multi-commodity flow problem and use ILP to solve it. Then, we relax the non-crossing constraints and transform the ILP model into an LP model to reduce the runtime. we also construct a crossing graph according to the intersection of routing paths and propose a heuristic algorithm to locate congestion quickly. Finally, we reduce the local area capacity and allow global automatic congestion optimization. Compared with the state-of-the-art work, experimental results show that our method can reduce the routing time by 60% and handle larger-scale PCB escape routing problems.

A novel Soft Actor–Critic framework with disjunctive graph embedding and autoencoder mechanism for Job Shop Scheduling Problems

The Job-Shop Scheduling Problem (JSSP) is a well-established and classic NP-hard combinatorial optimization issue. The quality of its scheduling scheme directly affects the operational efficiency of manufacturing systems. Priority Dispatching Rules (PDRs) are often utilized to address JSSP in real-world contexts, but the process of creating effective PDRs can be daunting and time-consuming. It also necessitates comprehensive domain knowledge, typically resulting in mediocre performance. In this paper, we introduce a novel reinforcement learning (RL) model called Disjunctive Graph Embedding with Autoencoder Mechanism for Job Shop Scheduling Problems (DGEAM-JSSP), designed to automate PDRs learning. Our proposed model confronts the issue using a Graph Neural Network (GNN) to learn node features that encapsulate the spatial structure of the JSSP graph representation. The ensuing policy network is size-agnostic, enabling effective generalization on larger-scale instances. Additionally, we employ a transformer encoder, incorporating parallel encoding and a self-attention mechanism, to successfully recognize long-term dependencies among operations in large-scale scheduling problems. We also implemented an end-to-end training approach using the Soft Actor–Critic (SAC) algorithm to instruct the two modules. Computational experiment results reveal that, with a single training, our agent successfully learns a superior dispatching policy, surpassing PDRs and state-of-the-art RL frameworks specifically tailored for each JSSP instance size in solution quality, as well as OR-Tools in execution speed. Moreover, results from random and benchmark instances illustrate that the uniquely-modeled learned policies have impressive generalization performance on real-world instances and significantly larger-scale scenarios involving up to 2000 operations.

An alternating direction multiplier method with variable neighborhood search for electric vehicle routing problem with time windows and battery swapping stations

This paper studies a real-world electric vehicle routing problem (EVRP). Specifically, it is an EVRP with time windows and battery swapping stations (EVRP_TWBSS). The EVRP_TWBSS considers the routing of electric vehicles (EVs), the determination of each electric vehicle’s battery level, and the selection of battery swapping stations. The criterion of EVRP_TWBSS is to minimize the operating costs. To simplify the structure of model, a time-discrete and multi-commodity flow model based on extended state-space-time network (TMFM_ESSTN) is established. Meanwhile, an alternating direction multiplier method with variable neighborhood search (ADMM_VNS) is presented to address the TMFM_ESSTN. In ADMM_VNS, the augmented lagrangian relaxation (ALR) model constructed from the TMFM_ESSTN is decomposed and linearized to a series of least cost vehicle routing subproblems through the linear augmented lagrangian relaxation (LALR) decomposed technique. Then, each subproblem is iteratively solved by using the dynamic programming and two special designed VNS strategies in ADMM_VNS iterative framework. The solution’s quality can be controlled to a certain extent through monitoring the gap between the lower and upper bounds obtained after each iteration. Test results on instances with different scales and a real-world instance based on partial road network in Kunming City demonstrate that ADMM_VNS can achieve smaller gaps and better solutions than several state-of-the-art algorithms. In which, ADMM_VNS can reduce the optimal gap by up to 2.27 % compared to the other state-of-the-art algorithms in small-scale instances. The gap of ADMM_VNS is calculated based on the lower bound and the upper bound in the large-scale instances and the real-world instance are 10.36 % and 1.57 %, respectively.

On the impact of co-optimizing station locations, trip assignment, and charging schedules for electric buses

As many public transportation systems around the world transition to electric buses, the planning and operation of fleets can be improved via tailored decision-support tools. In this work, we study the impact of jointly locating charging facilities, assigning electric buses to trips, and determining when and where to charge the buses. We propose a mixed integer linear program that co-optimizes planning and operational decisions jointly and an iterated local search heuristic to solve large-scale instances. Herein, we use a concurrent scheduler algorithm to generate an initial feasible solution, which serves as a starting point for our iterated local search algorithm. In the sequential case, we first optimize trip assignments and charging locations. Charging schedules are then determined after fixing the optimal decisions from the first level. The joint model, on the other hand, integrates charge scheduling within the local search procedure. The solution quality of the joint and sequential iterated local search models are compared for multiple real-world bus transit networks. Our results demonstrate that joint models can help further improve operating costs by 14.1% and lower total costs by about 4.1% on average compared with sequential models. In addition, energy consumption costs and contracted power capacity costs have been reduced significantly due to our integrated planning approach.

Optimising distributed heterogeneous flowshop group scheduling arising from PCB mounting: integrating construction and improvement heuristics

ABSTRACT In real-world manufacturing systems for processing printed circuit boards (PCBs), the workshops integrating various flowline-based cells are common in large-scale enterprises. The scheduling problem within the systems is modelled as the distributed heterogeneous flowshop group scheduling problem (DHFGSP) in this study. Departing from practical requirements and considering the grouping characteristics among PCB components, we account for carryover sequence-dependent setup time (CSDST). Moreover, recognising the critical importance of just-in-time production in semiconductor manufacturing, the total tardiness, a previously unexplored objective within the DHFGSP context, is addressed. To tackle this problem, a mixed-integer linear programming (MILP) model, capable of obtaining optimal solutions for small-scale instances, is proposed. Due to the NP-hard nature of the problem, obtaining high-quality solutions in a reasonable time using the MILP model becomes challenging for large-scale instances. Therefore, a solution algorithm, comprising construction and improvement heuristics, is developed. Capitalising on the problem’s characteristics, the construction heuristic efficiently generates high-quality feasible solutions in a very short time. Built primarily around artificial bee colony (ABC) optimisation, the improvement heuristic can significantly further enhance solutions by integrating the collaborative and restart operators. Comprehensive experiments on instances of varying scales demonstrate the effectiveness of the proposed algorithm for the problem under investigation.

A Ramsey-Type Equilibrium Model with Spatially Dispersed Agents

AbstractWe present a spatial and time-continuous Ramsey-type equilibrium model for households and firms that interact on a spatial domain to model labor mobility in the presence of commuting costs. After discretization in space and time, we obtain a mixed complementarity problem that represents the spatial equilibrium model. We prove existence of equilibria using the theory of finite-dimensional variational inequalities and derive a tailored diagonalization method to solve the resulting large-scale instances. Finally, we present a case study that highlights the influence of commuting costs and show that the model allows to analyze transitory effects of industrial agglomeration that emerge and vanish over time as in the real economy.